Merge pull request #5 from kolosovpetro/MATH-95

MATH-95

Author: kolosovpetro

BIBTEX-CITATION.bib

@@ -1,8 +1,8 @@
-@misc{kolosov2023polynomial,
+@misc{polynomial_identity_with_binomial_theorem_and_faulhabers_formula,
     title = {{Polynomial identity involving Binomial Theorem and Faulhaber's formula}},
-    author = {{Kolosov, Petro}},
+    author = {Kolosov, Petro},
     journal = {Figshare},
     number = {https://doi.org/10.6084/m9.figshare.2386},
     note = {\url{https://kolosovpetro.github.io/pdf/PolynomialIdentityInvolvingBTandFaulhaber.pdf}},
     year = {2023}
-}
+}

CHANGELOG.md

@@ -5,6 +5,15 @@ All notable changes to this project will be documented in this file.
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning v2.0.0](https://semver.org/spec/v2.0.0.html).
 
+## [1.1.0] - 2025-01-23
+
+## Changed
+
+- Update references
+- Update citation
+- Fix environments
+- Update explanations on coefficients A
+
 ## [1.0.3] - 2024-10-18
 
 ## Changed

out/PolynomialIdentityInvolvingBTandFaulhaber.bbl

@@ -15,13 +15,14 @@
   \href{https://www.linkedin.com/pulse/problem-triangle-developing-polynomial-function-f-n-m-albert-tkaczyk/}{\texttt{LinkedIn}},
   2018.
 
-\bibitem{kolosov2022106}
+\bibitem{unusual_identity_for_odd_powers}
 {Kolosov, Petro}.
 \newblock {106.37 An unusual identity for odd-powers}.
 \newblock {\em {The Mathematical Gazette}}, 106(567):509--513, 2022.
+\newblock \url{https://doi.org/10.1017/mag.2022.129}.
 
 \bibitem{abramowitz1988handbook}
-Milton Abramowitz, Irene~A Stegun, and Robert~H Romer.
+{Abramowitz, Milton and Stegun, Irene A. and Romer, Robert H.}
 \newblock Handbook of mathematical functions with formulas, graphs, and
   mathematical tables, 1988.
 
@@ -30,57 +31,56 @@ Alan~F Beardon.
 \newblock {Sums of powers of integers}.
 \newblock {\em {The American mathematical monthly}}, 103(3):201--213, 1996.
 
-\bibitem{kolosov2017third}
+\bibitem{oeis_numerical_triangle_row_sums_give_cubes}
 Petro Kolosov.
 \newblock {Numerical triangle, row sums give third power, Entry A287326 in The
-  On-Line Encyclopedia of Integer Sequences}.
-\newblock Published electronically at \url{https://oeis.org/A287326}, 2017.
+  On-Line Encyclopedia of Integer Sequences}, 2017.
+\newblock \url{https://oeis.org/A287326}.
 
-\bibitem{kolosov2018fifth}
+\bibitem{oeis_numerical_triangle_row_sums_give_fifth_powers}
 Petro Kolosov.
 \newblock {Numerical triangle, row sums give fifth power, Entry A300656 in The
-  On-Line Encyclopedia of Integer Sequences}.
-\newblock Published electronically at \url{https://oeis.org/A300656}, 2018.
+  On-Line Encyclopedia of Integer Sequences}, 2018.
+\newblock \url{https://oeis.org/A300656}.
 
-\bibitem{kolosov2018seventh}
+\bibitem{oeis_numerical_triangle_row_sums_give_seventh_powers}
 Petro Kolosov.
 \newblock {Numerical triangle, row sums give seventh power, Entry A300785 in
-  The On-Line Encyclopedia of Integer Sequences}.
-\newblock Published electronically at \url{https://oeis.org/A300785}, 2018.
+  The On-Line Encyclopedia of Integer Sequences}, 2018.
+\newblock \url{https://oeis.org/A300785}.
 
 \bibitem{alekseyev2018mathoverflow}
 {Alekseyev, Max}.
-\newblock {MathOverflow answer 297916/113033}.
-\newblock Published electronically at
-  \url{https://mathoverflow.net/a/297916/113033}, 2018.
+\newblock {MathOverflow answer 297916/113033}, 2018.
+\newblock \url{https://mathoverflow.net/a/297916/113033}.
 
 \bibitem{scheuer2023mathstackexchange}
 {Scheuer, Markus}.
-\newblock {MathStackExchange answer 4724343/463487}.
-\newblock Published electronically at
-  \url{https://math.stackexchange.com/a/4724343/463487}, 2023.
+\newblock {MathStackExchange answer 4724343/463487}, 2023.
+\newblock \url{https://math.stackexchange.com/a/4724343/463487}.
 
 \bibitem{bateman1953higher}
 Harry Bateman.
 \newblock {\em {Higher transcendental functions [volumes i-iii]}}, volume~1.
 \newblock McGRAW-HILL book company, 1953.
 
-\bibitem{kolosov2018numerator}
+\bibitem{oeis_numerators_of_the_coefficient_a_m_r}
 Petro Kolosov.
-\newblock {Entry A302971 in The On-Line Encyclopedia of Integer Sequences}.
-\newblock Published electronically at \url{https://oeis.org/A302971}, 2018.
+\newblock {Entry A302971 in The On-Line Encyclopedia of Integer Sequences},
+  2018.
+\newblock \url{https://oeis.org/A302971}.
 
-\bibitem{kolosov2018denominator}
+\bibitem{oeis_denominators_of_the_coefficient_a_m_r}
 Petro Kolosov.
-\newblock {Entry A304042 in The On-Line Encyclopedia of Integer Sequences}.
-\newblock Published electronically at \url{https://oeis.org/A304042}, 2018.
+\newblock {Entry A304042 in The On-Line Encyclopedia of Integer Sequences},
+  2018.
+\newblock \url{https://oeis.org/A304042}.
 
 \bibitem{kolosov2023github}
 {Kolosov, Petro}.
 \newblock {Polynomial identity involving Binomial Theorem and Faulhaber's
-  formula Source files}.
-\newblock Published electronically at
-  \url{https://github.com/kolosovpetro/PolynomialIdentityInvolvingBTandFaulhaber},
-  2023.
+  formula Source files}, 2023.
+\newblock
+  \url{https://github.com/kolosovpetro/PolynomialIdentityInvolvingBTandFaulhaber}.
 
 \end{thebibliography}

out/PolynomialIdentityInvolvingBTandFaulhaber.blg

@@ -7,30 +7,30 @@ Reallocating 'name_of_file' (item size: 1) to 42 items.
 Database file #1: PolynomialIdentityInvolvingBTandFaulhaber.bib
 You've used 14 entries,
             1791 wiz_defined-function locations,
-            521 strings with 6510 characters,
-and the built_in function-call counts, 2062 in all, are:
-= -- 178
-> -- 63
+            522 strings with 6486 characters,
+and the built_in function-call counts, 2024 in all, are:
+= -- 171
+> -- 56
 < -- 1
-+ -- 30
-- -- 16
-* -- 58
-:= -- 326
-add.period$ -- 41
++ -- 28
+- -- 14
+* -- 53
+:= -- 314
+add.period$ -- 42
 call.type$ -- 14
 change.case$ -- 13
 chr.to.int$ -- 0
 cite$ -- 14
 duplicate$ -- 83
 empty$ -- 266
-format.name$ -- 16
-if$ -- 478
+format.name$ -- 14
+if$ -- 466
 int.to.chr$ -- 0
 int.to.str$ -- 14
 missing$ -- 4
-newline$ -- 72
+newline$ -- 73
 num.names$ -- 14
-pop$ -- 75
+pop$ -- 82
 preamble$ -- 1
 purify$ -- 0
 quote$ -- 0
@@ -45,4 +45,4 @@ type$ -- 0
 warning$ -- 0
 while$ -- 18
 width$ -- 16
-write$ -- 143
+write$ -- 145

out/PolynomialIdentityInvolvingBTandFaulhaber.pdf

@@ -2,22 +2,19 @@
 
 @misc{abramowitz1988handbook,
     title = {Handbook of mathematical functions with formulas, graphs, and mathematical tables},
-    author = {Abramowitz, Milton and Stegun, Irene A and Romer, Robert H},
+    author = {{Abramowitz, Milton and Stegun, Irene A. and Romer, Robert H.}},
     year = {1988},
-    publisher = {American Association of Physics Teachers}
+    publisher = {{American Association of Physics Teachers}}
 }
 
 # binomial coefficients
 
-@article{graham1989concrete,
-    title = {Concrete mathematics: a foundation for computer science},
-    author = {Graham, Ronald L and Knuth, Donald E and Patashnik, Oren and Liu, Stanley},
-    journal = {Computers in Physics},
-    volume = {3},
-    number = {5},
-    pages = {106--107},
-    year = {1989},
-    publisher = {American Institute of Physics}
+@book{graham1994concrete,
+    title = {{Concrete mathematics: A foundation for computer science (second edition)}},
+    author = {{Graham, Ronald L. and Knuth, Donald E. and Patashnik, Oren}},
+    year = {1994},
+    note = {\url {https://archive.org/details/concrete-mathematics}},
+    publisher = {{Addison-Wesley Publishing Company, Inc.}}
 }
 
 # bernoulli numbers
@@ -45,15 +42,16 @@ @article{beardon1996sums
 
 # unusual identity odd powers
 
-@article{kolosov2022106,
+@article{unusual_identity_for_odd_powers,
     title = {{106.37 An unusual identity for odd-powers}},
     author = {{Kolosov, Petro}},
     journal = {{The Mathematical Gazette}},
     volume = {106},
     number = {567},
     pages = {509--513},
     year = {2022},
-    publisher = {{Cambridge University Press}}
+    publisher = {{Cambridge University Press}},
+    note = {\url{https://doi.org/10.1017/mag.2022.129}},
 }
 
 # Max ALekseyev's answer MO
@@ -63,7 +61,7 @@ @misc{alekseyev2018mathoverflow
     author = {{Alekseyev, Max}},
     journal = {{MathOverflow https://mathoverflow.net/a/297916/113033}},
     number = {297916/113033},
-    howpublished = "Published electronically at \url{https://mathoverflow.net/a/297916/113033}",
+    note = {\url{https://mathoverflow.net/a/297916/113033}},
     year = {2018}
 }
 
@@ -74,7 +72,7 @@ @misc{scheuer2023mathstackexchange
     author = {{Scheuer, Markus}},
     journal = {{MathStackExchange https://math.stackexchange.com/a/4724343/463487}},
     number = {{4724343/463487}},
-    howpublished = "Published electronically at \url{https://math.stackexchange.com/a/4724343/463487}",
+    note = {\url{https://math.stackexchange.com/a/4724343/463487}},
     year = {2023}
 }
 
@@ -98,50 +96,50 @@ @misc{tkaczyk2018continuation
 
 # OEIS triangles that row sums is odd power
 
-@misc{kolosov2017third,
+@misc{oeis_numerical_triangle_row_sums_give_cubes,
     title = {{Numerical triangle, row sums give third power, Entry A287326 in The On-Line Encyclopedia of Integer Sequences}},
     author = {Kolosov, Petro},
     journal = {{The On-Line Encyclopedia of Integer Sequences}},
     number = {A287326},
-    howpublished = "Published electronically at \url{https://oeis.org/A287326}",
+    note = {\url{https://oeis.org/A287326}},
     year = {2017}
 }
 
-@misc{kolosov2018fifth,
+@misc{oeis_numerical_triangle_row_sums_give_fifth_powers,
     title = {{Numerical triangle, row sums give fifth power, Entry A300656 in The On-Line Encyclopedia of Integer Sequences}},
     author = {Kolosov, Petro},
     journal = {{The On-Line Encyclopedia of Integer Sequences}},
     number = {A300656},
-    howpublished = "Published electronically at \url{https://oeis.org/A300656}",
+    note = {\url{https://oeis.org/A300656}},
     year = {2018}
 }
 
-@misc{kolosov2018seventh,
+@misc{oeis_numerical_triangle_row_sums_give_seventh_powers,
     title = {{Numerical triangle, row sums give seventh power, Entry A300785 in The On-Line Encyclopedia of Integer Sequences}},
     author = {Kolosov, Petro},
     journal = {{The On-Line Encyclopedia of Integer Sequences}},
     number = {A300785},
-    howpublished = "Published electronically at \url{https://oeis.org/A300785}",
+    note = {\url{https://oeis.org/A300785}},
     year = {2018}
 }
 
 # OEIS coefficients A
 
-@misc{kolosov2018numerator,
+@misc{oeis_numerators_of_the_coefficient_a_m_r,
     title = {{Entry A302971 in The On-Line Encyclopedia of Integer Sequences}},
     author = {Kolosov, Petro},
     journal = {{The On-Line Encyclopedia of Integer Sequences}},
     number = {A302971},
-    howpublished = "Published electronically at \url{https://oeis.org/A302971}",
+    note = {\url{https://oeis.org/A302971}},
     year = {2018}
 }
 
-@misc{kolosov2018denominator,
+@misc{oeis_denominators_of_the_coefficient_a_m_r,
     title = {{Entry A304042 in The On-Line Encyclopedia of Integer Sequences}},
     author = {Kolosov, Petro},
     journal = {{The On-Line Encyclopedia of Integer Sequences}},
     number = {A304042},
-    howpublished = "Published electronically at \url{https://oeis.org/A304042}",
+    note = {\url{https://oeis.org/A304042}},
     year = {2018}
 }
 
@@ -151,6 +149,6 @@ @misc{kolosov2023github
     title = {{Polynomial identity involving Binomial Theorem and Faulhaber's formula Source files}},
     author = {{Kolosov, Petro}},
     journal = {{GitHub}},
-    howpublished = "Published electronically at \url{https://github.com/kolosovpetro/PolynomialIdentityInvolvingBTandFaulhaber}",
+    note = {\url{https://github.com/kolosovpetro/PolynomialIdentityInvolvingBTandFaulhaber}},
     year = {2023}
-}
+}

src/PolynomialIdentityInvolvingBTandFaulhaber.bib

@@ -48,12 +48,10 @@
     \let\thefootnote\svthefootnote%
 }
 
-\newtheorem{thm}{Theorem}[section]
-\newtheorem{cor}[thm]{Corollary}
-\newtheorem{lem}[thm]{Lemma}
-\newtheorem{examp}[thm]{Example}
-\newtheorem{conj}[thm]{Conjecture}
-\newtheorem{defn}[thm]{Definition}
+\newtheorem{theorem}{Theorem}[section]
+\newtheorem{example}[theorem]{Example}
+\newtheorem{conjecture}[theorem]{Conjecture}
+\newtheorem{definition}[theorem]{Definition}
 
 \numberwithin{equation}{section}
 

src/PolynomialIdentityInvolvingBTandFaulhaber.tex

@@ -13,6 +13,6 @@
         7     & 1 & 37 & 61 & 73 & 73 & 61 & 37 & 1
     \end{tabular}
     \caption{Values of $6k(n-k) + 1$.
-    See the OEIS entry: \href{https://oeis.org/A287326}{\texttt{A287326}}~\cite{kolosov2017third}.}
+    See the OEIS entry: \href{https://oeis.org/A287326}{\texttt{A287326}}~\cite{oeis_numerical_triangle_row_sums_give_cubes}.}
     \label{tab:triangle_row_sums_give_cubes}
 \end{table}

src/figures/02_fig_triangle_row_sums_give_cubes.tex

@@ -13,6 +13,6 @@
         7     & 1 & 1081 & 3001 & 4321 & 4321 & 3001 & 1081 & 1
     \end{tabular}
     \caption{Values of $30k^2(n-k)^2 + 1$.
-    See the OEIS entry \href{https://oeis.org/A300656}{\texttt{A300656}}~\cite{kolosov2018fifth}.}
+    See the OEIS entry \href{https://oeis.org/A300656}{\texttt{A300656}}~\cite{oeis_numerical_triangle_row_sums_give_fifth_powers}.}
     \label{tab:row-sums-gives-fifth-power}
 \end{table}

src/figures/03_fig_triangle_row_sums_give_fifth_power.tex

@@ -13,6 +13,6 @@
         7     & 1 & 30157 & 139861 & 241753 & 241753 & 139861 & 30157 & 1
     \end{tabular}
     \caption{Values of $140 k^3 (n-k)^3 - 14k(n-k) + 1$.
-    See the OEIS entry \href{https://oeis.org/A300785}{\texttt{A300785}}~\cite{kolosov2018seventh}.}
+    See the OEIS entry \href{https://oeis.org/A300785}{\texttt{A300785}}~\cite{oeis_numerical_triangle_row_sums_give_seventh_powers}.}
     \label{tab:row-sums-gives-seventh-power}
 \end{table}